{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 7: Interpolation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Robert Johansson\n",
    "\n",
    "Source code listings for [Numerical Python - Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib](https://www.apress.com/us/book/9781484242452) (ISBN 978-1-484242-45-2)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams[\"font.family\"] = \"serif\"\n",
    "mpl.rcParams[\"font.size\"] = \"12\"\n",
    "\n",
    "mpl.rcParams['mathtext.fontset'] = 'stix'\n",
    "mpl.rcParams['font.family'] = 'serif'\n",
    "mpl.rcParams['font.sans-serif'] = 'stix'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from numpy import polynomial as P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy import interpolate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy import linalg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p1 = P.Polynomial([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{1.0} + \\text{2.0}\\,x + \\text{3.0}\\,x^{2}$"
      ],
      "text/plain": [
       "Polynomial([1., 2., 3.], domain=[-1,  1], window=[-1,  1])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p2 = P.Polynomial.fromroots([-1, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{-1.0}\\color{LightGray}{ + \\text{0.0}\\,x} + \\text{1.0}\\,x^{2}$"
      ],
      "text/plain": [
       "Polynomial([-1.,  0.,  1.], domain=[-1.,  1.], window=[-1.,  1.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.33333333-0.47140452j, -0.33333333+0.47140452j])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1.roots()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.,  1.])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2.roots()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 3.])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1.coef"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1,  1])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1.domain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1,  1])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1.window"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10.75, 24.75, 44.75])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1(np.array([1.5, 2.5, 3.5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# p1([1.5, 2.5, 3.5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\color{LightGray}{\\text{0.0}} + \\text{2.0}\\,x + \\text{4.0}\\,x^{2}$"
      ],
      "text/plain": [
       "Polynomial([0., 2., 4.], domain=[-1.,  1.], window=[-1.,  1.])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1+p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{-0.2}\\color{LightGray}{ + \\text{0.0}\\,x} + \\text{0.2}\\,x^{2}$"
      ],
      "text/plain": [
       "Polynomial([-0.2,  0. ,  0.2], domain=[-1.,  1.], window=[-1.,  1.])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2 / 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p1 = P.Polynomial.fromroots([1, 2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{-6.0} + \\text{11.0}\\,x - \\text{6.0}\\,x^{2} + \\text{1.0}\\,x^{3}$"
      ],
      "text/plain": [
       "Polynomial([-6., 11., -6.,  1.], domain=[-1.,  1.], window=[-1.,  1.])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p2 = P.Polynomial.fromroots([2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{-2.0} + \\text{1.0}\\,x$"
      ],
      "text/plain": [
       "Polynomial([-2.,  1.], domain=[-1.,  1.], window=[-1.,  1.])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p3 = p1 // p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{3.0} - \\text{4.0}\\,x + \\text{1.0}\\,x^{2}$"
      ],
      "text/plain": [
       "Polynomial([ 3., -4.,  1.], domain=[-1.,  1.], window=[-1.,  1.])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 3.])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p3.roots()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{-2.0} + \\text{1.0}\\,x$"
      ],
      "text/plain": [
       "Polynomial([-2.,  1.], domain=[-1.,  1.], window=[-1.,  1.])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "c1 = P.Chebyshev([1, 2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{1.0}\\,{T}_{0}(x) + \\text{2.0}\\,{T}_{1}(x) + \\text{3.0}\\,{T}_{2}(x)$"
      ],
      "text/plain": [
       "Chebyshev([1., 2., 3.], domain=[-1,  1], window=[-1,  1])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.76759188,  0.43425855])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c1.roots()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "c = P.Chebyshev.fromroots([-1, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{-0.5}\\,{T}_{0}(x)\\color{LightGray}{ + \\text{0.0}\\,{T}_{1}(x)} + \\text{0.5}\\,{T}_{2}(x)$"
      ],
      "text/plain": [
       "Chebyshev([-0.5,  0. ,  0.5], domain=[-1.,  1.], window=[-1.,  1.])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "l = P.Legendre.fromroots([-1, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{-0.6666666666666667}\\,{P}_{0}(x)\\color{LightGray}{ + \\text{0.0}\\,{P}_{1}(x)} + \\text{0.6666666666666666}\\,{P}_{2}(x)$"
      ],
      "text/plain": [
       "Legendre([-0.66666667,  0.        ,  0.66666667], domain=[-1.,  1.], window=[-1.,  1.])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75,  1.25,  5.25])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c(np.array([0.5, 1.5, 2.5]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75,  1.25,  5.25])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l(np.array([0.5, 1.5, 2.5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.array([1, 2, 3, 4])\n",
    "y = np.array([1, 3, 5, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "deg = len(x) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "A = P.polynomial.polyvander(x, deg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "c = linalg.solve(A, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2. , -3.5,  3. , -0.5])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f1 = P.Polynomial(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.1875"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1(2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "A = P.chebyshev.chebvander(x, deg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "c = linalg.solve(A, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.5  , -3.875,  1.5  , -0.125])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f2 = P.Chebyshev(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.1875"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f2(2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = np.linspace(x.min(), x.max(), 100)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(8, 4))\n",
    "\n",
    "ax.plot(xx, f1(xx), 'b', lw=2, label='Power basis interp.')\n",
    "ax.plot(xx, f2(xx), 'r--', lw=2, label='Chebyshev basis interp.')\n",
    "ax.scatter(x, y, label='data points')\n",
    "\n",
    "ax.legend(loc=4)\n",
    "ax.set_xticks(x)\n",
    "ax.set_ylabel(r\"$y$\", fontsize=18)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('ch7-polynomial-interpolation.pdf');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f1b = P.Polynomial.fit(x, y, deg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{4.187500000000003} + \\text{3.187499999999996}\\,\\left(\\text{-1.6666666666666667} + \\text{0.6666666666666666}x\\right) - \\text{1.687500000000004}\\,\\left(\\text{-1.6666666666666667} + \\text{0.6666666666666666}x\\right)^{2} - \\text{1.6874999999999973}\\,\\left(\\text{-1.6666666666666667} + \\text{0.6666666666666666}x\\right)^{3}$"
      ],
      "text/plain": [
       "Polynomial([ 4.1875,  3.1875, -1.6875, -1.6875], domain=[1., 4.], window=[-1.,  1.])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f2b = P.Chebyshev.fit(x, y, deg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x \\mapsto \\text{3.3437500000000004}\\,{T}_{0}(\\text{-1.6666666666666667} + \\text{0.6666666666666666}x) + \\text{1.9218749999999991}\\,{T}_{1}(\\text{-1.6666666666666667} + \\text{0.6666666666666666}x) - \\text{0.8437500000000021}\\,{T}_{2}(\\text{-1.6666666666666667} + \\text{0.6666666666666666}x) - \\text{0.42187499999999944}\\,{T}_{3}(\\text{-1.6666666666666667} + \\text{0.6666666666666666}x)$"
      ],
      "text/plain": [
       "Chebyshev([ 3.34375 ,  1.921875, -0.84375 , -0.421875], domain=[1., 4.], window=[-1.,  1.])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f2b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4659.738424139959"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.cond(P.chebyshev.chebvander(x, deg))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8542033440472896"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.cond(P.chebyshev.chebvander((2*x-5)/3.0, deg))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.        , -0.33333333,  0.33333333,  1.        ])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(2 * x - 5)/3.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f1 = P.Polynomial.fit(x, y, 1)\n",
    "f2 = P.Polynomial.fit(x, y, 2)\n",
    "f3 = P.Polynomial.fit(x, y, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = np.linspace(x.min(), x.max(), 100)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(8, 4))\n",
    "\n",
    "ax.plot(xx, f1(xx), 'r', lw=2, label='1st order')\n",
    "ax.plot(xx, f2(xx), 'g', lw=2, label='2nd order')\n",
    "ax.plot(xx, f3(xx), 'b', lw=2, label='3rd order')\n",
    "ax.scatter(x, y, label='data points')\n",
    "\n",
    "ax.legend(loc=4)\n",
    "ax.set_xticks(x)\n",
    "ax.set_ylabel(r\"$y$\", fontsize=18)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Runge problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def runge(x):\n",
    "    return 1/(1 + 25 * x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def runge_interpolate(n):\n",
    "    x = np.linspace(-1, 1, n + 1)\n",
    "    p = P.Polynomial.fit(x, runge(x), deg=n)\n",
    "    return x, p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "xx = np.linspace(-1, 1, 250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8, 4))\n",
    "\n",
    "ax.plot(xx, runge(xx), 'k', lw=2, label=\"Runge's function\")\n",
    "\n",
    "n = 13\n",
    "x, p = runge_interpolate(n)\n",
    "ax.plot(x, runge(x), 'ro')\n",
    "ax.plot(xx, p(xx), 'r', label='interp. order %d' % n)\n",
    "\n",
    "n = 14\n",
    "x, p = runge_interpolate(n)\n",
    "ax.plot(x, runge(x), 'go')\n",
    "ax.plot(xx, p(xx), 'g', label='interp. order %d' % n)\n",
    "\n",
    "ax.legend(loc=8)\n",
    "ax.set_xlim(-1.1, 1.1)\n",
    "ax.set_ylim(-1, 2)\n",
    "ax.set_xticks([-1, -0.5, 0, 0.5, 1])\n",
    "ax.set_ylabel(r\"$y$\", fontsize=18)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('ch7-polynomial-interpolation-runge.pdf');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Spline interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-1, 1, 11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = runge(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f = interpolate.interp1d(x, y, kind=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "xx = np.linspace(-1, 1, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "\n",
    "ax.plot(xx, runge(xx), 'k', lw=1, label=\"Runge's function\")\n",
    "ax.plot(x, y, 'ro', label='sample points')\n",
    "ax.plot(xx, f(xx), 'r--', lw=2, label='spline order 3')\n",
    "\n",
    "ax.legend()\n",
    "ax.set_ylim(0, 1.1)\n",
    "ax.set_xticks([-1, -0.5, 0, 0.5, 1])\n",
    "ax.set_ylabel(r\"$y$\", fontsize=18)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('ch7-spline-interpolation-runge.pdf');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.array([0, 1, 2, 3, 4, 5, 6, 7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = np.array([3, 4, 3.5, 2, 1, 1.5, 1.25, 0.9])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "xx = np.linspace(x.min(), x.max(), 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6MHXlER74cBUjFu3m6IXkW+7vVDaMjrPXc+KRYvgeTWHbY805vXdjHlUvhBDGutlq4v+6cjXxffv23XY18Q8//JDY2FjMZvN1x6hRowZ2dtdfJY+MjGTEiBEsWLAAB4ec778mt6gKgExLJmO/60PLT7fjka4JGP0Crk+8cNv9jGrgl5eUUjQIKk6DoOJXNQ78fstpmgeXZEDjIBoEed2w0Z9y8qDtpPVsKvcMznN2cu6Zvlwc9SK1Oz5nwJkIIUTeMXo18WPHjjFq1Ci++OIL3N3d+emnn+jcuXMOnd2lz9cyyThfS8tKY8w3z9Bh+n5crZpKU8fj2PjRW+6j80kDP6PEJGcwb1ME8zZG3HHjwGNLx3P6/TkUj4e459vR5PmJeVy1EKIoyQ9PURm1mnh6ejrly5fHz88PZ+fslh0VK1Zk5syZ19UoT1FdoTAFnKTMJN776kk6zzyBkwkqz5iKQ72Wt9zHYtWM/m0fczfmnwZ+Rrm2caBvMUd636JxYNz+lWx56QXKRsLpp+rQatS3BlQthCgK8kPAKQjuJ+AUzd98BUBCRgKjpj9O1y9O4GwLwXO+um24STdbeOG77czdGMGzTYKY9ETNIhtuABztbOhWrywrXmnKrF5hlC3uzAe/H+SBcasYu2Q/UfFpV433DGlB47k/cbyiiTI/bGfpC62xWq0GVS+EEOJ+FN3ffvlYijmFDz7rzDOzonBwguB587Gv0eiW+ySkmek1ewt/7D3H2+2qMKJtlXzVndhIJpOiRZVS/DCwIUtefJAWVUoyZ8NJmoxfzYvf72B3ZPzlsc6+IbT6diXHatkT9NcplvZ4gMyMVAOrF0IIcS8k4OQzaVlpvDfzSbp+E4WtqyL4+/9hFxx6y33OJ6bz5Bcb2X4qjqndauf77sRGquZXjClP1WbdsIfo92Agaw5e4NFp6+n6xUb+2n8eq1Vj5+5D27mbONHEnQrbEljxZCMy01KMLl0IIcRdkICTj5gtZsbO7cnjM49hZw/B33yHXWDVW+5z9EIynaZv4HRsKnN61+PRmr55VG3B9m/jwA0jmvN2uypExaXRf244D3/yN99ujiBT2dP2842cbu9L0MF0/nryATJSEowuWwghxB2SgJNPZFmzGPtDP9pO34uTguBZX2FXqdYt99l+Ko4un28gI8vCgmcbFrjuxPmBm6Md/RsH8ffQZkztVhtXB1ve+nkvD3y4io9XHqXOyKVEdQwg8HAmK59sTGpijNElCyGEuAMScPIBrTUTfn6R5lO34palqTxjym3n3FzZwO+nQtTAzyj/Ng5c/HwjFlzZOPCj1aysN54Tj5cn4KiZv59qRkr8eaPLFUIIcRuGNUdRSpmA34DNgD1QHuirtU67YkxvYBCQfumtWVrreXlcaq77as046k5ag1eapsLUD3Co3+qW4/9t4BdS2p05fQpnAz+jKKWoH1Sc+kHFOXohu3Hgou2RfK8H8/bDn9LwrwjWdm3Ox01GczTZCV8PJ4a2rkzH2gVn4VIhhLhXObGaOMDw4cNJTU2ldOnSbNy4kYkTJ1KpUqWcKxTjOxlv1FqPBVBKLQY6Adc2H3lKa30yrwvLK7/tW4jXB/PwidcEfvQGTs063XTslQ38GlcswefPhBapBn55rUJJV8Z1qs7rrSoxb1ME0ze+RkzjibRfd4oX145keK13iIqHEYuyVwGWkCOEuBcfbfmIg7EHc/SYwV7BvFHvjRw9JkC7du2YMGHCfR/H2dmZcePGoZTik08+YcKECTds9Hc/DPvtqLW2Av+GG1vAHzh0g6EvKKXOAc7ANK11bN5Vmbu2ntnM+XdG0eg0lHqpCy4d+tx0rDTwM05xVwdefrgSg5qWp8EHGlOjCbRfH8n7tmN5o9pI0szOTFh+SAKOEKJAMWo1cYB333338p+PHj1KSEhIzp/gnazImZs/QGtgGTD6BtsCAe9Lf24LrLzJMQYC4UB42bJlb7giaX5zPP64/qhvNb2/crCOfKPbLcemZWbpQfPCdcAbS/T7S/dri8WaR1WKa5V7Y4kOeGOJ/qRnE72/crBe+Gg1XX7YT7rcG0uMLk0IUYDIauJaHzx4UPft21d36NDh8jGuVaBXE9daL9datwEClVLPXbPthNY6+tLLVUBTpZTNDY7xpdY6TGsd5u3tnQdV35/Y9Fi+fr8rHdZnYRdWCt8P5t907LUN/N6UBn6G8vVwAmBy6WGsDvOk2qEs3jsyGl/365d+EEKI/Co/rCZeuXJlZs2aRceOHenVq1eOn6NhAUcpFaKUanfFWyeAIKWUl1LK/dKYcZduXwFUBE5orS15XWtOMlvNTPn0KbosScYa6Ej5r35HmW78r+Fcwn8N/KY8VUsa+OUDQ1tXxskuO2OP9xvBP7XcqLU/k6EH34ZCtq6bEKLwqlmzJseOHbv8+siRI9Sq9V9rkmtXEz98+DBw89XEhw8fzpAhQ6hfv/4Nj3GtK+fxBAYGcvz48fs+p2sZOUM1A+inlKoN2AFVgJeA4UAs8CFwDpihlDoBVAd6GFRrjvnil6G0//Y0Vk9FyNylKEfnG447eiGZXrO3EJ+ayZze9aTHTT7x7zybCcsPcSY+jamVR2OX9Rb1tySxcmgbWkxcbnCFQghxe61atWLTpk2MGDECrTUNGzakZcuWrFixgoiICKZNm3Z5NfH+/fvTt29fXnrpJby8vHB1dWX69OmMHz+eTz75hCFDhly1mvjhw4dZu3Yte/bsoVq1atetJg6wdetW3nrrLVxcXNi+fTtTpkzJ8XOU1cTz0LI9C9HPj8Q3QVNl3mzsazxww3HbT8XR9+ut2JoUX/epJz1u8rn3Fu+k8sweVD+aRXzvUBoOv/ktRyGEAFlN/E7JauIFwKGYg5wZOZqAC5qA4YNvGm7+beBXTBr4FRgj2tdgUavxHPNTuM7dxp45w4wuSQghijwJOHkgMTORxaO603C/FZeOtfHoNuSG4xZuPc3AeduoWNKNnwY/QEBxlzyuVNwLWxsTH/dsxsSGr3PBC8yf/MaJpZ8aXZYQQhRpEnBymVVbmf5pN9r9lYYlxI2yH1zbx/C/Bn7DftrNA+WL88PABtKduIDx9XDire7tGFO/D2kOcP7d6VzY9LPRZQkhRJElASeXfb/sfR6af5wML0XIrCXXPTFlsWpG/rqPCcsP8XhtP2b1qivdiQuoliGlaNGsPeMffAzbLDj42puknd5ndFlCCFEkScDJRXujwnGZ+B2OFk3VaZ9j8ix51fZ0s4UXv9/O3I0RDGwSxKQnakp34gLujUcqYw1qz9cPNcAzDjYM7Io1Jd7osoQQosiR36a5JMWcwup3+lM5CkoN6oRD7SZXbf+3gd/ve6SBX2HiYGvDtO61WVPsKf54qBy+J6ysefZhsFqNLk0IIYoUCTi5ZPa0Z3h4QwZZdb3xee6Dq7adT5QGfoVZQHEXPuxcneluz7O5njulw1PYNKKD0WUJIcR9W7p0KYGBgZeb/d2rQYMG0axZs8s/e/bsyZkCryCTPXLB7+tmEDbvIMklFKGf/XLVtisb+M3uXZfGFfP/0hLi7rWv4cv6ozGM2TKMiRVHUfnX4xws9xLBg6caXZoQIp8598EHZBzI2dXEHaoE4/Pmmzl6TMi51cR9fHz4/PPPc6Cim5OAk8MiYo6SNvZT/DM1FT6fjMnd6/K2Kxv4LXi2ofS4KeRGdghhe0QcHzsO5d2ED/GesYLzFedQ6uGbrxovhBB5xcjVxJOSknj//fextbXFxcWFQYMGYWubw5HkTlbkLEg/oaGhN1yRNC+YLWb92aBQvb9ysD4x/vmrtq08cE5Xfvt33WT8Kn3yYrJBFYq8duR8og5++w/db8IUvaFOsF5fP1inndxjdFlCCIMV9dXEt23bps1ms9Za66FDh+oxY8bcsM4CvZp4YfLj/FdosiaFlOruBLz2362IheGnGTBXGvgVRRVKujHmsar8dbE8G7q1wi0RNg16Cp2eYnRpQogizOjVxOvUqXP5ik3z5s1ZtWpVjp+jBJwccujUVkp+/hdprlB7+iKUyfRfA7//SQO/oqxLqD+P1/bjs5hWbHk0kFInLGx8obWsPi6EMIzRq4kPHTr0qs+uUKHCfZ/TtWQOTg4wW81sfHMA9WPB871B2Hj7YbFqRv+2j7kbI+hYy5fxXaTHTVGllGJsx2rsOh3P5xlDcAwdQZ1/YjgwaSBVXp9pdHlCiCLI6NXEo6OjGT58OM7Ozhw6dIiPP/44x89RVhPPAQum96HG1E0kN/Kh7qzVpJstvLpwJ7/vOcfAJkEMbxMsPW4E+84k8Pj0DTQI0HRd8DplzmlKTxxKyTZ9jS5NCJHHZDXxOyOriRvowKHV+M3ZRLyXInTyIhLTpYGfuLGqvsV4p10V1h7THB4wnCQnOP7uBDIjDxldmhBCFDoScO6D2WJm15sv4ZECFUaPIFo70fVzaeAnbu6ZBgE8Us2H6btKcHxwe5xTYPPAJ9BZ5tvvLIQQ4o5JwLkPiyc9Q819WaS2DiKh5uN0mr6B07GpzO5dl8dq+RldnsiHlFJ82LkGPsUc+fxCG8I7+FHiuJntrz9udGlCiDxW2KaI5LT7/X4k4NyjE4f/wf+H3UT7mLB94Su6fL6BjCwLC55tKN2JxS0Vc7JjWvc6XEjMYEPwSHZUt8Nx2TFOfzfe6NKEEHnE0dGRmJgYCTk3obUmJiYGR0fHez6GTDK+B1prfupai8r7Mrn4zisM3l+GUu6OzO1bT3rciDs2c+1x3v/9AEObKip+8BrFk6DKD/NxDg41ujQhRC4zm81ERkaSnp5udCn5lqOjI/7+/tf10LnTScbymPg9WPnFi1Tdk8mxRiUZssefkNJuzOlTV3rciLvS78FANh6PYco/Fxnz0jMUHzufnYN60WDZVkyOTkaXJ4TIRXZ2dgQGBhpdRqEmt6juUszZQzjOXkm0Fwzzep4Hyhfne2ngJ+6ByaSY+ERNvFzs+fzkA+x6qiKe5yyEPycrjwshxP0yLOAopUxKqaVKqXeVUmOVUt8rpZyuGeOolJqmlBqhlJqtlKpkVL2/7Iii0Yer+O2lp/BMhIW1m9IqtCKzetXF1UEuhIl74+Viz5SnanEqNpUd5d5hY30H3DZEcWL2+0aXJoQQBZrRV3A2aq3HaK3fBpyBTtdsfxk4pbUeB3wCzMrrAiE73IxYtIfqZ76j7p50dlZ1YlmxR2lSyVu6E4v7Vj+oOC8/XInfdl2AXh9zzBcSJs8n5eBOo0sTQogCy7Dfzlprq9Z6LIBSyhbwB67teNYO2Hhp/B6gplLKPU8LBSYsP4TKiOfJ8PXEu8HHgS+RZdVM+vNwXpciCqnnH6rAA+WLM351BukvdMdsgj2De2LNzDS6NCGEKJAMv/yglGoNLAGWaK2vffypJJB0xevES+9de4yBSqlwpVR4dHR0jtd4Jj6NquY92GXB4rq1iLH1vvy+EDnBxqSY/GQtXB1s+TKiCTs7+1PsrJmdQ7oaXZoQQhRIhgccrfVyrXUbIFAp9dw1my8Able8dr/03rXH+FJrHaa1DvP2zvkeNL4eTmx1eICBzUay0P2Zq94XIqeUdHfk4661OHw+maPB77G+rg1Oqw9x6vvpRpcmhBAFjpGTjEOUUu2ueOsEEKSU8rriNtRSoOGl8dWBXVrrxDwulaGtK+NkZ0Oq6b+s5WRnw9DWlfO6FFHINankzXPNyrNgWwzOPcdwtDTEfvgpaSePG12aEEIUKEZewckA+iml3lZKjQaqABOB4cC/V3KmAAFKqbeB14B+RhTasbYf4zpVx8/DCQX4eTgxrlN1OtaW5RhEznu1ZSXCAjx5f50zGf1bkgXsGtgVbZb1qoQQ4k5JJ2Mh8qGo+DTaTllHGU9H2p99naY/J5HVpSnVx35udGlCCGGoO+1kbPgcHCHE9fw8nJj4RE32nkniYuj7bKoOpv/9TfTaFUaXJoQQBYIEHCHyqZYhpejbKJCvwjNxf+ppznlBxGuvYI6NNbo0IYTI9yTgCJGPvfFIZar7FWPM3npEdSqNfaqFHc93lxWIhRDiNiTgCJGPOdjaMK17bSxWzQqnoaxtonDbEcGxLz8xujQhhMjXJOAIkc8FFHdhXKfqrDttxenBZ9l/FHLKAAAgAElEQVQdBGlTZ5J86IDRpQkhRL4lAUeIAqBDTV+61SvLe3sqYNe+IikOsP/53rKUgxBC3IQEHCEKiJEdQqhcyo0pF/uys6XCLTKRve8NM7osIYTIlyTgCFFAONplz8e5YHYkxq8P62tp7H5cTvTalUaXJoQQ+Y4EHCEKkIql3BjzWFVmngnB54EKRBaHU0NfJSsuzujShBAiX5GAI0QB0yXUn8dr+/Hu2Wc487AV+6RMdr42UB4dF0KIK0jAEaKAUUrxXsdqeBT3Yb9dd/5uZMVlw14ivptjdGlCCJFvSMARogBydbDl0+61+Tm9HoGVA9hfFhLGTyL99CmjSxNCiHxBAo4QBVRV32K8064KIy/2xvRgJllY2f1iP7TFYnRpQghhOAk4QhRgzzQIoG61yvyd+SQbm2bhdjCSQ5+NN7osIYQwnAQcIQowpRQfdq5BuGsLAr3LsK0ymL+YS9Le3UaXJoQQhpKAI0QBV8zJjk+71+G9tP6UCksn0QkODHkWa0aG0aUJIYRhJOAIUQjULutJ3zb1+S2tG3sfysAtKp49Y98wuiwhhDCMBBwhCon+DwaRVOEx/JzLsb4W2P+4nOj1a4wuSwghDCEBR4hCwmRSTHqyNp/ZD6ZKSCpnPeHksNewJCcbXZoQQuQ5CThCFCJeLvaM6tachRnPcLpZGs6xqex46yWjyxJCiDwnAUeIQqZ+UHHKP9QLD9sKrKurcVm+kTPLFhtdlhBC5CkJOEIUQs83r8jvfq8TWj6diJJw9p13MMfEGF2WEELkGcMCjlKqvFLqe6XUUKXUFKXUuzcY01sptUkptebSTw8jahWioLExKd7r3ozv1EASG6dgl2pm+9BnZUFOIUSRYeQVHC/gB631BK31EOAppVToDcY9pbVudulnXh7XKESBVdLdkcefGoAy1WB9AyvuG/Zx8se5RpclhBB5wrCAo7XeqrW+cmKACUi5wdAXlFKvK6XeVUp55VF5QhQKTSp5E1V/JA3KmjniB/HjJpBx7qzRZQkhRK7LF3NwlFKPA8u11gev2fQ38JHWeiIQDvx4k/0HKqXClVLh0dHRuVytEAXL84+E8mux1zA9kARZFra/0l9uVQkhCj3DA45S6iHgIeCVa7dprU9orf9NLKuApkopmxuM+1JrHaa1DvP29s7dgoUoYOxsTPTv3Zckm4ZseSALjx3HOfLNdKPLEkKIXGVowFFKtQNaA0MAH6VUQ6WUl1LK/dL2cUop20vDKwIntNYWg8oVosDy83DC+/HxhJW24UAApH78GakRJ4wuSwghco2RT1GFAguABsBqYDFQGRgOPHdp2DlghlLqTeBNQJ6iEuIePVwzkG3BY3Grl4gFza6X+6OtVqPLEkKIXKEK2734sLAwHR4ebnQZQuRLGVkWfpz0IhkRf/LAKjusL/Wm6nOyKKcQouBQSm3TWofdbpzhc3CEEHnHwdaGB/uMo0pJd/aUB8v0b0g8fMDosoQQIsdJwBGiiClXshhpLafhE5pMuq1mzysD0VlZRpclhBA5SgKOEEVQi0YPEFNmIAcaZ+J17CK7Jo82uiQhhMhREnCEKKLa9BxBQKly7KoENrP/R+zeHUaXJIQQOUYCjhBFlJODLWWfmYVvrQySHeHAK4PRmZlGlyWEEDnijgOOUupVpdR0pdQTSimH3CxKCJE3gsqVQzf4gIjG6XidTmDrR/JElRCicLibKzg9gX3AdqCnUmqAUsold8oSQuSVJo88iXf5h9gZonH+bhnnwtcbXZIQQtw329sPyaa1rnXFy2OXwk1vpVS81vrbnC9NCJEXlFLU7zeV8LgGJJyykPDai3gv34CNo6PRpQkhxD27pzk4SilvoAXgDQxRSv2jlKqSo5UJIfKMq4sr/p1nc7ZJOl7n09g4+iWjSxJCiPtyN3NwKiqlRiultpO9hMJPQFtgI/AV0EIp1SV3yhRC5LYK1erhV7c/O6pb8fx5HRH/LDO6JCGEuGd3fIsK2AJkkr1+1JvAOq11ypUDlFJllVLPaq2/yMEahRB5pMGTI0g9uYqLp84QP3QYfisaYevqZnRZQghx1+7mFtUKIEhr/ZLWetm14QZAa30KWK6U+iDHKhRC5BllMlH32e+IedCCR5yZNW/0M7okIYS4J3cTcKbdKNTcQBNg4D3WI4QwmLtXKao+MZndtS34rdzDoT8WGF2SEELctTsOOFrrtXc4dDnw5L2VI4TIDyo3aItP84c56wUx744hPS7G6JKEEOKu5HgnY631ea31ypw+rhAibzXtM4W4ps64J1tZ9VI3o8sRQoi7Iks1CCFuyGRrR/MXF7I3zErg1tNs+Xaq0SUJIcQdk4AjhLgpT9/yBPcYxulSwMQZxJ85aXRJQghxRyTgCCFuqVarfqS2CcYhE/4Z/CRaa6NLEkKI25KAI4S4rQ6v/8D+BjaUP5TI8kmvGV2OEELclgQcIcRt2dg50PStbznhByXn/sGp/eFGlySEELckAUcIcUd8g2ri0Cf7aaq9Q/pitVgMrkgIIW7OsICjlCqvlPpeKTVUKTVFKfXuDcY4KqWmKaVGKKVmK6UqGVGrECJbi2fe5VAzbwJPm/mkb1sChy+l0Yer+GVHlNGlCSHEVYy8guMF/KC1nqC1HgI8pZQKvWbMy8AprfU44BNgVl4XKYS4mkP32RwOVLQMP0VY2j9ExacxYtEeCTlCiHzFsICjtd6qtV58TS3XLgXRjuzVytFa7wFqKqXc86hEIcQNTFpziulVe5PmAIO2/YKLNZE0s4UJyw8ZXZoQQlyWL+bgKKUeB5ZrrQ9es6kkkHTF68RL7127/0ClVLhSKjw6OjoXKxVCnIlP45BtVX6pXw3fizAsYsLl94UQIr8wPOAopR4CHgJeucHmC4DbFa/dL713Fa31l1rrMK11mLe3d+4UKoQAwNfDCYDvi/VmW4gTYbvSeDrla7zdHAyuTAgh/mNowFFKtQNaA0MAH6VUQ6WU1xW3oZYCDS+NrQ7s0lonGlOtEAJgaOvKONnZADCu/Gtc9IC2m/dSNnUne6MSDK5OCCGyGfkUVSiwAGgArAYWA5WB4cBzl4ZNAQKUUm8DrwH9DChVCHGFjrX9GNepOn4eTqTaePBt484US4Lue2fT54u/WHdEbhMLIYynClvb9bCwMB0eLk3IhMhLK4Z2xv+3/Wxt4cp7HqOY+EQtHqvlZ3RZQohCSCm1TWsddrtxhs/BEUIUfM0/+J4zZR2oui6Z1xwXMOSHnXy17rjRZQkhijAJOEKI+2ZjZ0+1z75BKSi3egsvBp5k7NIDvL90P1Zr4bpKLIQoGCTgCCFyRKmKNcl6uScBZxTlNnzKi6GOzFx3glcX7iQzy2p0eUKIIkYCjhAix9TrM4LI+mUI3qKou38Eb7QM5JedZ+j3zVZSMrKMLk8IUYRIwBFC5KgmUxeQ4GELvyfRMXoi47vUYMOxGLrN3MTF5AyjyxNCFBEScIQQOcqhmCc+E8bjlQgbvl/P49ZlzOwZyuHzSXSesYGImGtXZBFCiJwnAUcIkeOCHnyE+B6tCTlk4pfZH9Hc6TjfDWhAYpqZzjM2SENAIUSuk4AjhMgVjYZ/zLmQklT8x44Ns3pTp1gq/xv8AA62Njz5xUb+OXLR6BKFEIWYBBwhRK5QJhP1pn9HpqMNaStNnP22G+U9bFn03AOU8XKmz9dbWLwzyugyhRCFlAQcIUSucfHxw2vcaHxi4O9V58la8gql3BxY8GxD6pT1lIaAQohcIwFHCJGrKrTsTMKTLai518RPK5fBphkUc7Ljm771aFvdh7FLD/DB7wekIaAQIkdJwBFC5LqG70wmumIJKq515J8l78PRv3C0s+HTbnXo2TCAL9ce57Ufd2G2SENAIUTOkIAjhMh1ytaWOjPmY7WzIf1vd04t6AcXj2BjUox+tCpDW1fm5x1R9PsmXBoCCiFyhAQcIUSecPUPoPhHYyl9ETaEO5P2XVdIi0MpxfMPVWB85xqsP3pRGgIKIXKEBBwhRJ4JfLgjab0fpeYBWLA/Gf1jH7BkX7HpWrcMX/bIbgjYZcYGTsWkGlytEKIgk4AjhMhTocPGcbFWAKFrbVmybxv8+fblbS2qlOLb/g2ITzPTacZ6aQgohLhnSuvC9eRCWFiYDg8PN7oMIcQtZMbGsKN9CzKzMvBoE0P1DuOgbr/L249eSKbX7C3Ep2byRY8wHqxYwsBqRV7SWmOOiiLj8GGyLl7EEhNDVkwsltgYrJmZmBwcUU6OmBwcMTk7Yefnj0PFCjiUL4+Nh4fR5Ys8oJTaprUOu+04CThCCCNEb9/EuR59OFLGROMHzuPdfQFUaHF5+/nEdHrN3sKx6GQmPlGTx2r5GVityC3WtDRSNm0ibecu0vfuJX3vXiwJV1+5M7m5YevlhXJwwJqRjk5Lx5qRgU5NRZvNl8fZeJfAMbgKro0b49r8Iez9/fP6dEQekIAjhMj3Dn49Df3hZ2yqa8PTIQnY91sBJYMvb09IMzNwbjibT8Tydrsq9G8cZGC1IqdkxcSQvGYNSStXkbJhAzo9HWxscKhUCadqVXGsWg3H4MrYliqFjZcXJgeHGx5HW61knT1LxtGjl36OkbZrF5nHs5tHOlSsgGuzh3Bv1xbH4OAbHkMUPBJwhBAFwpahA3H7bR0bWkPfQFvUgNXg8t8tqXSzhVcW7OSPvecY2CSI4W2CMZmUgRWLe6HNZpJWriJ+4QJSNm4CrbEtXRq3Fi1wa9Ecp9q1MTk65shnZUZEkLR6Ncmr15C6bRtkZeFcty5evXri+tBDKBubHPkcYQwJOEKIAkGbzWzs2gaXw2c49lg6ncpXhJ6/gt1/v+wsVs2oX/cxb1MEj9f246PONbC3lWckCoLMyCjif/yR+EU/YYm+iG3p0ng83hG3hx/GoUoVlMrdsGqJjyf+p0XEfjufrDNnsfP3x6vHM3h07YrJySlXP1vkDgk4QogCIzPmIjs7tMScmY5N21gaVG8LnWeB6b8Qo7Xms9VHmfjnYRpXLMHnz4Ti4mBrYNXiVtIPHSLmiy9I/GMZKIVrkyZ4PPkkWfWqE2dOIN2STqYl8/I/7W3scbVzxdnOGVc7V9zs3XCyzbkAorOySPprJbHz5pG2bRu2Pj6UfO1V3Nu1Q5kkLBck+T7gKKV8gLFATa113RtsbwZMBuIvvbVUaz3hdseVgCNEwRS/dycR3bpzqqSiepNzlGv0Ijw86rpxC7eeZsTPewgp7c6cPnUp4Xrj+Rki7/yyI4oJyw9xJj6NRubzvHTuH9y2bcTqZM+xpuXYGObIIYc4zqTHkGLNvOPjejl64e/mj7+rP/5u/gQWC6Rq8aoEuAdgUvceSlK3buX8uA9J378fx5o18BkxAqdate75eCJvFYSA0wXIAEbeqNBLAQet9Zq7Oa4EHCEKrhO/fEv68LFsq2ZL2+qReLX7GML6XDdu5YHzPP/ddkq5OzK3bz0CirsYUK2A7HAzYtEeKsVtp8+BxVSOSiTFAZbWNfFHmMLqoPHLysLfnIVflgXfrCxKWCw4ao3DpR97rclUihSlSDGZSDaZSHB0I8rVi0h7RyIxc86ciEVnr1XmaudKSPEQqpaoSlipMMJKheFs53xXdWurlYTFvxL98cdkRUfj/mgHfN58Ux41LwDyfcCByyFm4i0CTg/gAOAOzNRan77dMSXgCFGw7Zk4EtuvFvJPI3t6BJzGsdsCqNjyunHbIuLo981WbE2Kr/vUo5pfMQOqLcLS4rh48Dc++20OFXeep+Z+TaojrK4LZ6uAFx50qhRGZZ862Lr5gJMnOHll/9POCbQFrP/+mCE1BpLOQdLZ7H/GRcD5PXDhAFgyMQPHXT3Z71uVvW6e7LOmcijxBFnWLGxNttTyrkVD34Y08m1ESPGQO57bY01J4eJXXxHz1SxsPT0pPe4DXBs1yt3vTtyXwhBwSgLOWuuTSqmqwE9AiNb6uuWGlVIDgYEAZcuWDY2IiMjdwoUQuUZrTfiQPrj+uZm/29gx0Psipr5/QOma142VhoB5LC0OfWApG/fOZ2HcMUrutKPtVo2Nhq0h7vxe4SH26PpkYA+AvY2Jan7uhAZ4EhrgSZ2ynpR0v8snpSxmuHgYzu6GiH/g6CpIOgNAeomKbA9qwCY3TzbFH+JA7AEAfFx8eLjsw7Qq14qa3jXv6HZW+v79RA0dRuaxY3j26EHJ117Nsae6RM4q8AHnBmPPAfW11rdML3IFR4iCT5vNbH66Ay57I9je0UQvryzovwI8yl43VhoC5jKrBY78SdrWWSy5sJnvXJ0pddSWniuteKbAunJVmFWxI+ddil+1m5ezPV3C/NkWEceeqAQys7L/29Tf0+mqwBPs44atzV3Mp9Eaog/BsZVweDmcXAfaCr51iK36GP94eLPi/CY2RG0g05qJt5M3rcu1pmOFjlT2qnzrU01P58Kkj4mbNw/78uXxmzRR+ufkQwUy4CilXMi+ahOtlBoOfKm1jlVKeQFHAV+tdfqtjikBR4jCISsxkfBOrbCLTiCyo5nHvD2h73Jw9rpubEKamQFzw9kiDQFzTmos7JhH6tav+E7H83WxYrjFQv9lJkIizWRWqETF98fwp7UEIxbtIc1subyrk50N4zpVp2Pt7LCZkWVh35lEtkfEsS0iju2n4jifmHF5bM0yxS6HntplPPF0sb/zOhPPwt7/we4FcG4PmGyhUhuSqz/BWgcbVpxexd+Rf2O2mgn2Cuax8o/RNqgtXo7X/z36V/L69Zwd8SaWpCR8x32Ae5s29/YdilyR7wOOUqop0BNoA8wAJgF9gepa60FKqaeAdsB+IAT4QWu99HbHlYAjROGRFnmafZ3bk6YzyWybQgv/ytBzMdhfP6H0yoaAzzYJ4g1pCHhv4k/Bukmk7f6BhU52fOnhRYbFSpdVHrTfFYfJxZXSr72KxxNdLjfMu/IpKl8PJ4a2rnw53NyI1pozCenZYedS4Nl3JhGLNfv3UZC3C3XKel4OPRW8Xe/s3+X5/bDrO9j1A6REg6sP1OpGfMij/JF4iMVHF7MvZh+2JlseLvsw3YK7Ubtk7RvO18mKjibypSGk7dhBiecGU+KFF+Rx8nwi3wec3CIBR4jCJX7PDk706EGssxXnlrE0DH4Ius4Dm+t74FzbEHB8lxrY3c3tj6IsIQrWTSRz+zz+5+rMNI/iJNlkUfOALy/9nYRbXBweT3TB+9VXsfX0zPGPT8u0sDsynm2n4tgeEc/2U3HEpmQ/Uu7maEvtsp7UKetBaIAntcp44OZod/ODWczZt692zIcjf2ZPaC7TAGo/zWG/GvwcsZzFRxeTZE6ikmclngp+inaB7a57Esuamcm50aNJ+GkRrg+3wPfDj7BxlSf2jCYBRwhRaFzYtJazAwZx1hN8WlykVp1u0H4y3OC/vKUh4F1Kjoa1E9Db5rDWwY7RXqWJtsvEMz6At7a6UzZ8B/ZBQZR+bwzOoaF5VpbWmpMxqZdvaW07GcfhC0lonf2vvXIpN+pcmscTGuBJueLON35yKulc9hWdHfMh5gjYOUNIR1JrdOH3rFh+OLSAQ3GHcLN3o2ulrjxd5Wm8nb2vqiNu3nzOf/QRDkFBlPnic+x8ffPsexDXk4AjhChUzqxcSsxLr3OitIlKD54nuOmr8NCbNx2/YOsp3vx5L1V93ZndWxoCXseSBeGzsK4ayzFrBsO8AjnqnIqdpQSvRz9I6KIVWFNTKTFwIMWfHYjJ/i7mxeSSxHQzu07Hs+3SXJ6dp+JJysgCwMvFnjplPS6Hnpr+HjjZX7HmlNYQuTU76OxdBJlJ4FEWXaMbO8rUZH7USv6K+Asbkw3tg9rTK6QXFTwrXN49ZcMGIoe8jMnVlbKzZuEQFJjXpy8ukYAjhCh0Ihb/QPLw0RwsZyKswTkCWo+FBoNvOv7fhoA+7o7M7VufssXvrhlcoRWxgYxfX8Uce5C3PMqzqpgZG+VIz2Jd6LTkMGn/rMepdm1KvzcGhwoVbn88g1itmiMXkrOv8Fyaz3P8YgoAtiZFiK87dcp6Xgo9Hvh5OGVf5clMhYNLYee3cHwNoCGgEaeD2zDXGsMvJ34n3ZJOE/8mDKg+gFols7scpx84wKn+A8BqpczMmThVq2rcyRdhEnCEEIXSkflfkDV2MnsqmKhX9xzlHvsUanW/6fj/GgKa+LpP3SLdEFCnxBD9v1fxPvEL3zqX4pPixci0zaC1/6O8fCaQlE+mo4GSr76KZ/duBXJSbWxKJjtOxV0OPbtOJ1x+wquUu8PlW1p1Ajyp6uuOQ8pZ2PU97PweYo+BrRPxwa35oXgpvj2/kfiMeOr71GdAjQHU86mHOSKCU337YUlIwH/6dFzq1zP4jIseCThCiELr4FeT0RO/YH+golbDi5R/YjZUaX/T8UcvJNFr9lYS0sx8/kxokWsImJllJXzF9wRveYuLNqm8XKIip50SqeQRzKiAgbh/PJ/ULVtwbtiA0u+9h72/v9El55gsi5WD55L+m8sTEUdkXBoA9rYmqvsVy568XNaDenbH8Tq6CPb+BOnxpLqV5sfAWnyTGUV0Rjw1vWsyqOYg6tlU4HT//phPncZv8ie4NW9u8FkWLRJwhBCF2uG5MzCPm8qRMoqqjeOo+PT3ENTspuPPJaTTe052Q8BJXWvxaM3CP1E0Ic3Mj+v3U3LDKFrrVUzwKMv/PGxwsnPipZov0HKrmYuTp6BsbSn5xjA8unS54yUOCrILien/3dY6Fc+eyAQyLdmNCMt4OVHX34VHnXZTJ345bqdXk6mzWOxbiVnOtpzJSqaGdw2eL9eT0qNmkb7/AP5TJuPWooXBZ1V0SMARQhR6RxbMInPURI77QcVmyQT3WAABD9x0/JUNAd9pH0K/BwvnRNHTsanM+ucEx8KXM059RpRTCiN9yxGlU2gb2JZXSnQl/b1JpO3YgUvTJpQePRo7Hx+jyzZMRpaFvVGJ7LgUerZFxHEhKbsRoa99Cv09d/KIZQ0lkvfxi5srM0t4cxYLdV2q8Mr8ZGyPnSby5VGMiva8415A4t5JwBFCFAnHFs0j7e0PiCgFZR5Kpkb3OVDh4ZuOTzdbePmHnSzbV/gaAu44FcdX606wbG8Ug2yW0M/+f0ws5ctvjuDv6s87dd+k0vKDXPx0GsrJCZ+33sS9Q4cicdXmbmitiYpPY/up+KsaEZbVZ+hos56OdhvY4prElx4eJGaZGPuDDaXOZzGqfj+2l8peDuLabs4i50jAEUIUGSeWLCRp+Ehi3MCmRTJNun8GIY/edLzFqhn5617mbzpFp9p+fFSAGwJarJoV+8/z1brjhEfE4eeYwRyPWRzK2s4Ebx+SlKZX1d70tm9K7Mj3yNh/ALeWLfF59x1svb1v/wECgNTMLHZHJrD9VBzbT8aSdWoLTTNXoz128LOjA4N/BP+LMKdJA34p1gmNCT8PJ9YPl/k5OU0CjhCiSDm3cQ2RL7yA1WLhfKtUOnT/EGp1u+l4rTXTVh1l0orDNKnkzYyn6xSohoCpmVn8b1sks/85wcmYVPw9nXi9egY1j77B+/bpbHZyoEaJGrxbZzie3/1JzOw52Hh64vPOO7i1ailXbe6T1poTF1PYduICvy2eS4DTnzRZFod3PPzcEewdgtmQ2oKfRg/C0b7g/L0qCCTgCCGKnITjh9jXuxuuMWnsfyidrs8Mx9Tg2Vvus2DrKUYs2kM1v2IFoiHghaR05m6IYP7mCOJTzdQs48HAxkG0yPyLb9a/y5fFXHCwc+blsNdpG1+W8++OIjMigmKdO1Fq2DBsihXdx+RzS6MPVxEVn4ZP5lk+Wj8N17QMRj5jQyXXNDrG2pHo1hKH2k9QL6whxZxvscSEuCMScIQQRVJGbAybez+O9+FottfPomPnR3BpNwlsbv6L5a/953nh+/zdEPDw+SS+WnecX3acwWy10rJKKQY0CSKsjBublzzH+xfWcdLejtb+zRha6QWyPp1F4q+/YVemDKXHjMalYUOjT6HQ+mVH1OUV1UukxvPxuqnYkc7oXnDWw0q75BQGx8eTlOnPHo8W2NfsTMOwMHyKORpdeoEkAUcIUWRZMjL458XulFy7n0PlNDU6+BLUeyG43Lz/TX5sCKi1ZsOxGGauO86aQ9E42pl4IrQMfR8MJLCECxdiDjNxSU/+IIUyNs6MaDSOqhvPEf3JZKzp6RTv348SAwdicnIy+lQKvStXVA8lgVF/Tcbe053lw5rwzbnFZFnNtE6z5ZXok/hYLOy0lmeb20PYVX+cB+rUokJJV6NPocCQgCOEKNK01myb+SH2U+aS7ASZrUw0e/F7KF3jpvtc2RDwix6hNKpgTEPAzCwrS3afYea6Exw4m0gJVwd6NQzgmQYBeLrYY7b+v707ja+qPPc+/ruyM5AJAklIQCDMEG0AFVQQRdQjrQPOFMUJHFqt2vZYHvto69DHx1q1anvaqqhtHSrYUxCOE87KIKgMgjILIcwQEpIQMu99nRcJiAiKlmQlm//3FWtl7bUubj5k//e976GWiR8/wl+WPUMtzjVZQ7k062qK772fqs8+I+mEE8i+4w7tlxSgykWLKLhqLPFdu5L02IM8mf88k1dNJgZjZKse/HBdAX13rgBgXqQ3cxNPJuaocxlydD/6d2qjMVJfQwFHRATYsGAWa2++gbZFtaw4vo6zb7yd+GOv3O9O5FC/IOCVf/2INdubfkHA0spanv9wHU9/sJYtZVX0ap/CtSd1Z+SAjrSKC+HuzNwwgwdm/Zq1NTs4sSbCL/veStzUxZS98gqhzAyybv0lrc86U2+QzUD5zFmsv/56ko4+ms5PPsHm2u08vuhxpq2eRkIogdE53+eiciPls1dpV76SiBvzvDez4oYS7nsOgwfkcXz3di12hl9jUcAREWlQXVbCjBtH0emj9RR0dHJG5pB79dOQuv/F7Zp6QcD1xRX8dXY+L3y8ntmvaOwAABUSSURBVIqaMCf2TOfak7ozrHfmnqCyascqHph7D3O2LaBrTS3jvSN9i4dTPHEyAO3GjSXjmmuISU5u1Frl2yl96WU2jR9P6zPPpOODD2AxMawtXctjix/j1TWvkhibyJjcMVyZdSLxy96gZtEU2uysDzvzvRfvxAyhuudZHDcgj5N7Z5KkGVkKOCIie3N35jx5L3F/+Qetqp11x0Y49eZfkzhwzH57c5piQcDdC/O99tlmYswY2b8jV5/UjaM6fjH+Z3P5Zh5f/DgvrppCciTCT7bv4j92nU7Jm8sIFxXR+pxzaP+fPyeuQ4dDWpscOkVPPsm2B39P+rXX0P6WW/acX1OyhkcXPcrra18nOS6ZS3Mv5fLcy0krL6R28RSqFk0mtbT+a6yFkZ68yfHsyPkBx/QfwOm5WbRNjg/qrxQoBRwRkf0o3ryWObeOo/tHmyls67Q5pwv9r38C2uZ85dpwxLnrf5bw7NyCQ7Yg4L4L86W2iuXS47swdki3L82q2bprK098+gSTV07GPMwPi8oYszKTisWxhItLSB4ymMyf/YzEfgceUyTNg7uz5Te/oWTiJLLvvIO2l3x5faZVO1bx6KJHeavgLRJjExnddzRXHHkF6YnpULSa8JKpVH4yhZTizwD4LNKVNyKD2NjhDL43YBBnHJXNEWmHz0ByBRwRka/x4bTHqb7vj2TuiLChS4Tu5x5Pj6sehuT0L13n7vz53c958I1/b0HAypow/5q/nqf2Wphv3IndGDWoMyl73W9T+SaeXfos/1zxApFIHaMKy7nkE6dmZVvCZZUkDT6BzJ/8hKSB3/j7XZoRr6tjw403UT5jBp3+/CdShw//yjWf7/icCZ9OYHr+dBJCCVzc52KuPPJKspKz6i/YsRZf+j9ULJpK8rb59a+JdGR6ZBCr04fTPe9ERuR1oFf7lKgeg6WAIyLyDXbuLOLdB24m66UFtK6ETTlOr1Gn0+Xy30H8l8eyfNcFAQ+0MN+Io7KIbegNcnfmb53P88uf5+11b2PuXFFQzciPqqkrSMZrI/XB5oYbSBo06JC3gzSNSEUFBZdfQfWaNeQ88wyJed/b73X5pfk8sfgJXs1/FTPj7O5nM/aosXRP6/7FRWWbYfnLVC56kYRNc4nxMBs9nTfCA1mcMpSsvOH8x/c6cXTntKjZa203BRwRkYNUWLSeGQ/+jM7Tl5JaCVs7OelD+3Lk2LsI5QzYc923WRDwgAvz5bTd8+m6tLqUtwreYtKKSSwvXk6HyhDXLqqg/2dhwoXxWEI8bc49j7ZjxtCqT+9GbwdpfHWFhawdfQmRmmq6TZpE3BEH3oxzY/lGnl7yNC+uepGqcBWndj6Vsd8bS//M/l/uoakohpXTqf50KqH894iNVLPDU3g7cgxz408g+cgzODWvK4O7pxMf2/JnZDX7gGNm2cA9QH93/8pHEjOLAe4FyoEc4Cl3n/tN91XAEZHvavO2Ncx88Kdkv/85maVQFe+U5bai97kXkH3eTVhS2z0LAoYjTm6H1ny+rZziXTUckZbIL87oTWZqK56YuYb3VxaSEBvDxQM7cfXQ7nTLqO8RKq0u5Z117/B6wet8uGkurXbVcdbKGM74tILUjbHgRlzHLNqOuYK0Cy8glJYWcKvIoVa9ejVrR19CXHY2Oc//g1Bq6tdeX1xVzPPLnmfi8omU1ZRxVPpRXHbkZYzIGUHcvit0V5fD6neoWfISrJxOfG0ZVR7HzEgeM2OOI9zzDIb0P5JT+mS2qL3X9tYSAs5FQDVw5/4KNbPRwMnufoOZtQPmArnuHv66+yrgiMi/a2dVGTOnPkLZi1Pps7SSVrVQ0cop6xxHYm4OqcefyT2bc5mzoeJLrzPAgYyUeK4Y3JUxx3ehmiIWFy5m8fbFLN76CVvyl9BzfR3Hrof+BXWkFtd/oo7LSKX12SNpPfICEnJzo3oMhcCuOXNYd+11JB93HJ0ffwyL++Y9qipqK3hp9Us8t+w51patJTMxk1F9RnFhrwvJTNrPzvDhWij4gLqlL1O79GUSKzYRwVgY6ck7PpDSzqeTN2AQpx+ZTXoz34Ntb80+4ACY2SnAgwcIOM8Cb7j7sw3Hi4HL3H3x191TAUdEDqXVGxYz/7n78E+Wk7W2kqyS+vPVsVDaGkpTYyhLjqU4JZGK+BAeE6Z1UgxVXktlbQ1JpbVklkL7Uier1EmoqQ8uMfFGYs8OJB03mOQfXESrfv0Vag4zJZMns/n2X5E2ahTZd9910P/+EY/wwaYPeG7pc8zeNJuQhRjWaRgX9b6IIR2HEIoJffVF7rDlU8LLX6Xq05dIbpiRVRBpz9uRY1mfOYxOA07ljLzOdG7X/PZi21s0BJzXgUfdfWrD8SzgLnd/az/XXgdcB9ClS5djCwoKGrVuETk81YRrWPrJa6x7cxLbFq6gTXkNaTvDtNkJqZX7f0043olpE0tKemvis9sT36MXSaddSEL/QVhoP29EcljZ9tDDFE2YQPvx40m/ety3fv3a0rVMWTWFaaunUVxVTIfkDpzX8zzO7HYmXdt0PfALSzfgK6ZT/unLJG6YTazXUOZJzIj0Y1nqEFLzfsCwAX3pm53a7IJ3NAQc9eCISLN14n3vsLHki1TTtq6UNuEKMtok8sKPhkBMCIuLJ6Zt1gG3hRDxSISN/3kLO6dP54g//IHWI874TvepDdfyzvp3mLxyMnM3z8Vxctvlclb3sxjRdQTZyftftRuoH7ez5j12fvoyoc/fJKlmO2E3FnovFiQMgl4jGDBwKMd2bUeoGczIapEBx8ySgSR3L9QYHBFpzqYu3Mj/nfIplbVf/EpKjAvx2wvyOO/oA8+MEdlXpKqKdVeNpWrZMnKe/juJAwZ884u+xtZdW5m+djqv5b/GkqIlGEZeZh7DOg3j5E4n06dtnwP3ykQisPkTdn32ClVLXiW9bCkAm70dc2KOobzzcHIG/YDj+3alVVwwPZDNPuCY2TDgCuD7wKPA74FxQJ67/7hhFtVvgQqgC/CEZlGJSHMydeFGHnh9BZtKKumYlsj4EX0UbuQ7qSsuZu0PRxPZtYuukyYS36XLIblvQVkBr+W/xnvr32NJ0RIAspKyGHrEUAZlD+KY9sfQIeVrtvnYuZXKZdPZ8ckrtN0yi8TILmo8xAJy2ZQ5lLR+ZzJw0GBaJ9ZvG9EU/yeafcBpLAo4IiLSElXn51Mw+hJC7drRdeLzh3yJgMKKQmZtnMWMDTOYs3kOu2p3AZCdnM3R7Y+mX0Y/eqT1oEdaDzITM7/ayxOupSb/AzbPf4mE/LfJrloDwEbPYGXq8axrO5j/yu/I9rovthxpjF5NBRwREZEWpmLePNaNHUdi//50/utTxMQ3zoaadZE6Vu1YxYJtC1i4bSELty5kW+W2PT9PjU+le5vudEjuQHpiOu1atSO9VTppCWmEYkIYRmTXdopWfsTODfOIqVzDrlCYIg9xzGuJvNezH//d+nIAjkhLZPYvTz1ktR9swGmZq/yIiIhEoaSBA+lw771sGj+ezbfdTsf7f4fFHPrVh2NjYslNzyU3PZcxuWNwd4qqilhTsobVpatZXbKaNaVrWFa8jOLKYnbW7jzwzZKB5BQAvr8Auq+rY2avmj0/3lRygCmGjUwBR0REpBlpc87Z1G7cSOEjjxCb1Z6s8eMb/ZlmRkZiBhmJGRzX4biv/Lw6XM2Oqh2UVJcQ8QjujuNEPEJCKIH0xHTOf+hjzprx/1jeNoVJKV9Mee8Y0E7nCjgiIiLNTPqPrqNu21aKn/orsekZpI8bG2g9CaEEspOzv3a6+W8S1pNVuYM/Dbhgz9IIiXEhxo/o01RlfokCjoiISDNjZmTdfjt1RcVsu/9+YjPSaTNyZNBlHZDX1ND51Rco69GXzb2PxkqrAp9ZqIAjIiLSDFkoRMcH7md9SQmbbrudUNu2pJx0UtBl7VfJ1KnUbtpE7wl3Mvvkk4MuB4CWv2+6iIhIlIqJj6fTn/9EQq9ebLj5p1QuWhR0SV/hNTUUPfY4rfr1I7kZBTAFHBERkWYslJJClwmPE5uRwbprr6NyyZKgS/qS3b03mTf+pFntW6WAIyIi0szFZmbS5W9/IyYlmXXjrqZq2bKgSwKab+8NKOCIiIi0CPGdjiDnmWeISUpi3dhxVK1YEXRJzbb3BhRwREREWoz4Tp3IefrvWKtW9Rt0rlwZWC21W7ZQ+PuHSOzfv9n13oACjoiISIsS36VLfciJi9uzC3lT87o6Nt7yC7y2lg73/bbZ9d6AAo6IiEiLE5+TQ5en/47Fx1Mw5jLKZ85q0ucX/vG/qJw/n+y77yahW7cmffbBUsARERFpgRK6daPrCy8Ql5PD+h//mB3//GeTPLd85iyKJkwg7eKLaHPO2U3yzO9CAUdERKSFistqT86zz5I8ZAhb7riTbQ89jEcijfa82q3b2HTrrST06kXWbbc12nMOBQUcERGRFiyUkkznR/9C2qhRFE2YwMZbbiFcVnbIn+PhMJvGjydSWckRjzxMTGIwm2geLAUcERGRFs5iY8m++y7a/+IWdr7xJmtGnntIx+WEy8rYcONNVHz0Edl33EFCjx6H7N6NRQFHREQkCpgZ6ddcQ9dJE4lJTmb9tdey+dd3EC7f9W/dt2r5cvIvupjymTPJuv120s4/7xBV3LgUcERERKJIYl4e3aZMJv2aqymZPJn8kSMpe+01vLb2W9+rdNo01o6+BK+qIueZZ2h3+WWNUHHjMHcPuoZDauDAgT5v3rygyxAREQlcxcKFbL79V9SsWUNsZiZpo0aRNmoUcVntD/gaD4ep/OQTSv41mdIXXyRp0CCOePghYjMymrDyAzOz+e4+8BuvU8ARERGJXh4OUz5jBjuen8iumTMhNpaUU4aR0LMnsRmZxGZkEJuZQV3hdsrffZfy998nXFICsbG0u/IK2v/851hsbNB/jT0ONuA0n4pFRETkkLNQiNThw0kdPpyaggJ2THqBsunTKX/3PQiHv3RtTJs2pAw7mdThw0keOpRQamowRR8CgfbgmNnpwAXANsDd/e59fn4V8GOgquHUU+7+7NfdUz04IiIi38zDYcIlJdRt307d9u3EJCSQOGBAs+qt2Z9m34NjZknAY8BR7l5tZpPN7DR3f3ufS0e7+9qmr1BERCR6WShEbHo6senp0KdP0OUcckHGtMFAgbtXNxzPBs4C9g04N5rZFiAJ+JO7FzdhjSIiItICBRlw2gM79zouazi3t/eBV9y90MzOBP4bOG3fG5nZdcB1AF26dGmcakVERKTFCHIdnG3A3qOXWjec28Pd8929sOHwHWCYmYX2vZG7T3D3ge4+MDMzs9EKFhERkZYhyIAzB8gxs4SG4xOBV8ysnZm1BjCz35rZ7l6mXkC+u4f3cy8RERGRPQL7isrdK8zseuCPZlYILHb3t83sfqAYuA/YAjxqZvlAHnB5UPWKiIhIyxHoXDB3fxN4c59z/2evP/+hyYsSERGRFk97UYmIiEjUUcARERGRqBN1e1E1jOcpaMRHZADbG/H+LYHaoJ7aQW2wm9qhntpBbbBbY7ZDjrt/45TpqAs4jc3M5h3MEtHRTG1QT+2gNthN7VBP7aA22K05tIO+ohIREZGoo4AjIiIiUUcB59ubEHQBzYDaoJ7aQW2wm9qhntpBbbBb4O2gMTgiIiISddSDIyIiIlFHAUdERESiTqBbNbQkZnY6cAH1O567u98dcElNzsyygXuA/u4+KOh6gmBmPahvgwVAJ6DI3X8TbFVNz8xigJeAD4F4oAcwzt0rAy0sAGaWSH07vOHuvwi6niCY2VygquEw7O6nBVlPUMysD3AJUAkMA+5y94+CrarpmFlX4G1gfcOp1tTvM3lVEPUo4BwEM0sCHgOOcvdqM5tsZqe5+9tB19bEhgLTgAFBFxKgdsAkd58GYGZLzewVd58fcF1BmOPu9wCY2TTqPwD8I9iSAnEPsDDoIgI23d3vCrqIIJlZCHgIOMfdI2b2DFAXcFlNbSfwI3d/C8DM7maf/SabkgLOwRkMFLh7dcPxbOAs6pPqYcPd/2VmpwRdR5Dc/eN9TsUAu4KoJUjuHqH+jR0zi6W+N2tFoEUFwMwup/73QT8gJeBygpRnZrcCicDH7v5K0AUFYBBgwE0NH4qLgCeCLalpuXsRsDvcJAAD3f3OoOpRwDk47alPpruVNZyTw5iZnQ+87u7Lg64lKGY2Avg58LK7zwu6nqZkZkcCue5+m5n1C7qegP3O3T9q6MWYYWY73X1G0EU1sRzqPwxf4u6lZvYcUAP8PdCqgnMpMDHIAjTI+OBsA1L3Om7dcE4OU2Y2HBhO/Zv7YcvdX3f37wPdzOyGoOtpYucDVWb2S+q/vj3OzH4WcE2B2D3OxN3DwEzq/28cbsqA5e5e2nA8CzgluHICdzHwQpAFqAfn4MwBcswsoeFrqhOBvwRckwTEzM4CTgJ+CnQwsxx3nxNwWU2qofei215fReQD3QMsqcm5+//f/WczawWkuPsjAZYUCDPrC5zo7k81nOoFTAmwpKB8CKSbWagh6OUAKwOuKRANHwA/cPfaIOtQwDkI7l5hZtcDf2zYrXzxYTjAGDMbBlxO/Zv6r4DfH26zZszsWOo/lcwD3gWSgT9TH4IPJ9XA1WZ2NBAH5AI3B1tSMMzsQuBkIN7MLnH3QLvlA1AGnG1mHanv3V5PwF9NBMHdixvGIT3S8D6RCRx2MywbXAfcFHQRWslYREREoo7G4IiIiEjUUcARERGRqKOAIyIiIlFHAUdERESijgKOiIiIRB0FHBEREYk6CjgiIiISdRRwREREJOoo4IiIiEjUUcARERGRqKOAIyIiIlFHAUdEWhwzO8PMnjWzQjPLNLNEM5tiZvlmZkHXJyLB02abItIimVkaUAiMBTpRv4N1B3efG2hhItIsKOCISItlZh8DScBF7r4s6HpEpPnQV1Qi0pLNBioVbkRkXwo4ItIimVkM0A3IM7PEoOsRkeZFAUdEWqprgPuBeGAwgJmlBlqRiDQbsUEXICJysMysA3AkEAG2uvtsM1sGnG9mmcACYGeQNYpI86AeHBFpSU4A/gkMdvdpDef+BowBat19VWCViUizollUIiIiEnXUgyMiIiJRRwFHREREoo4CjoiIiEQdBRwRERGJOgo4IiIiEnUUcERERCTqKOCIiIhI1FHAERERkaijgCMiIiJR538BpBkv+GY8ZSAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "\n",
    "ax.scatter(x, y)\n",
    "\n",
    "for n in [1, 2, 3, 5]:\n",
    "    f = interpolate.interp1d(x, y, kind=n)\n",
    "    ax.plot(xx, f(xx), label='order %d' % n)\n",
    "\n",
    "ax.legend()\n",
    "ax.set_ylabel(r\"$y$\", fontsize=18)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=18)\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('ch7-spline-interpolation-orders.pdf');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multivariate interpolation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regular grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = y = np.linspace(-2, 2, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def f(x, y):\n",
    "    return np.exp(-(x + .5)**2 - 2*(y + .5)**2) - np.exp(-(x - .5)**2 - 2*(y - .5)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X, Y = np.meshgrid(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# simulate noisy data at fixed grid points X, Y\n",
    "Z = f(X, Y) + 0.05 * np.random.randn(*X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "f_interp = interpolate.interp2d(x, y, Z, kind='cubic')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "xx = yy = np.linspace(x.min(), x.max(), 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ZZi = f_interp(xx, yy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "XX, YY = np.meshgrid(xx, yy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(12, 5))\n",
    "\n",
    "c = axes[0].contourf(XX, YY, f(XX, YY), 15, cmap=plt.cm.RdBu)\n",
    "axes[0].set_xlabel(r\"$x$\", fontsize=20)\n",
    "axes[0].set_ylabel(r\"$y$\", fontsize=20)\n",
    "axes[0].set_title(\"exact / high sampling\")\n",
    "cb = fig.colorbar(c, ax=axes[0])\n",
    "cb.set_label(r\"$z$\", fontsize=20)\n",
    "\n",
    "c = axes[1].contourf(XX, YY, ZZi, 15, cmap=plt.cm.RdBu)\n",
    "axes[1].set_ylim(-2.1, 2.1)\n",
    "axes[1].set_xlim(-2.1, 2.1)\n",
    "axes[1].set_xlabel(r\"$x$\", fontsize=20)\n",
    "axes[1].set_ylabel(r\"$y$\", fontsize=20)\n",
    "axes[1].scatter(X, Y, marker='x', color='k')\n",
    "axes[1].set_title(\"interpolation of noisy data / low sampling\")\n",
    "cb = fig.colorbar(c, ax=axes[1])\n",
    "cb.set_label(r\"$z$\", fontsize=20)\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('ch7-multivariate-interpolation-regular-grid.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(6, 5))\n",
    "\n",
    "c = ax.contourf(XX, YY, ZZi, 15, cmap=plt.cm.RdBu)\n",
    "ax.set_ylim(-2.1, 2.1)\n",
    "ax.set_xlim(-2.1, 2.1)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=20)\n",
    "ax.set_ylabel(r\"$y$\", fontsize=20)\n",
    "ax.scatter(X, Y, marker='x', color='k')\n",
    "cb = fig.colorbar(c, ax=ax)\n",
    "cb.set_label(r\"$z$\", fontsize=20)\n",
    "\n",
    "fig.tight_layout()\n",
    "#fig.savefig('ch7-multivariate-interpolation-regular-grid.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Irregular grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.random.seed(115925231)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = y = np.linspace(-1, 1, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X, Y = np.meshgrid(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def f(x, y):\n",
    "    return np.exp(-x**2 - y**2) * np.cos(4*x) * np.sin(6*y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Z = f(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "N = 500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "xdata = np.random.uniform(-1, 1, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ydata = np.random.uniform(-1, 1, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "zdata = f(xdata, ydata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "c = ax.contourf(X, Y, Z, 15, cmap=plt.cm.RdBu);\n",
    "ax.scatter(xdata, ydata, marker='.')\n",
    "ax.set_ylim(-1,1)\n",
    "ax.set_xlim(-1,1)\n",
    "ax.set_xlabel(r\"$x$\", fontsize=20)\n",
    "ax.set_ylabel(r\"$y$\", fontsize=20)\n",
    "\n",
    "cb = fig.colorbar(c, ax=ax)\n",
    "cb.set_label(r\"$z$\", fontsize=20)\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('ch7-multivariate-interpolation-exact.pdf');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def z_interpolate(xdata, ydata, zdata):\n",
    "    Zi_0 = interpolate.griddata((xdata, ydata), zdata, (X, Y), method='nearest')\n",
    "    Zi_1 = interpolate.griddata((xdata, ydata), zdata, (X, Y), method='linear')\n",
    "    Zi_3 = interpolate.griddata((xdata, ydata), zdata, (X, Y), method='cubic')\n",
    "    return Zi_0, Zi_1, Zi_3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, 3, figsize=(12, 12), sharex=True, sharey=True)\n",
    "\n",
    "n_vec = [50, 150, 500]\n",
    "\n",
    "for idx, n in enumerate(n_vec):\n",
    "    Zi_0, Zi_1, Zi_3 = z_interpolate(xdata[:n], ydata[:n], zdata[:n])\n",
    "    axes[idx, 0].contourf(X, Y, Zi_0, 15, cmap=plt.cm.RdBu)\n",
    "    axes[idx, 0].set_ylabel(\"%d data points\\ny\" % n, fontsize=16)\n",
    "    axes[idx, 0].set_title(\"nearest\", fontsize=16)\n",
    "    axes[idx, 1].contourf(X, Y, Zi_1, 15, cmap=plt.cm.RdBu)\n",
    "    axes[idx, 1].set_title(\"linear\", fontsize=16)\n",
    "    axes[idx, 2].contourf(X, Y, Zi_3, 15, cmap=plt.cm.RdBu)\n",
    "    axes[idx, 2].set_title(\"cubic\", fontsize=16)\n",
    "\n",
    "for m in range(len(n_vec)):\n",
    "    axes[idx, m].set_xlabel(\"x\", fontsize=16)\n",
    "    \n",
    "fig.tight_layout()\n",
    "fig.savefig('ch7-multivariate-interpolation-interp.pdf');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Versions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%reload_ext version_information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.6.8 64bit [GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)]</td></tr><tr><td>IPython</td><td>7.5.0</td></tr><tr><td>OS</td><td>Darwin 18.2.0 x86_64 i386 64bit</td></tr><tr><td>scipy</td><td>1.2.1</td></tr><tr><td>numpy</td><td>1.16.3</td></tr><tr><td>matplotlib</td><td>3.0.3</td></tr><tr><td colspan='2'>Mon May 06 14:36:10 2019 JST</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.6.8 64bit [GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE\\_401/final)] \\\\ \\hline\n",
       "IPython & 7.5.0 \\\\ \\hline\n",
       "OS & Darwin 18.2.0 x86\\_64 i386 64bit \\\\ \\hline\n",
       "scipy & 1.2.1 \\\\ \\hline\n",
       "numpy & 1.16.3 \\\\ \\hline\n",
       "matplotlib & 3.0.3 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Mon May 06 14:36:10 2019 JST} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.6.8 64bit [GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)]\n",
       "IPython 7.5.0\n",
       "OS Darwin 18.2.0 x86_64 i386 64bit\n",
       "scipy 1.2.1\n",
       "numpy 1.16.3\n",
       "matplotlib 3.0.3\n",
       "Mon May 06 14:36:10 2019 JST"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%version_information scipy, numpy, matplotlib"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py3.6",
   "language": "python",
   "name": "py3.6"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
